Optimal Co-linear Gaussian Beams for Spontaneous Parametric Down-Conversion

I investigate the properties of spontaneous parametric down-conversion (SPDC) involving co-linear Gaussian spatial modes for the pump and the photon collection optics. Approximate analytical and numerical results are obtained for the peak spectral density, photon bandwidth, pair collection probability, heralding ratio, and spectral purity, as a function of crystal length and beam focusing parameters. I address the optimization of these properties individually as well as jointly, and find focusing conditions that simultaneously bring the pair collection probability, heralding ratio, and spectral purity to near-optimal values. These properties are also found to be nearly scale invariant, that is, ultimately independent of crystal length. The results obtained here are expected to be useful for designing SPDC sources with high performance in multiple categories for the next generation of SPDC applications.Comment: 15 pages, 8 figures. Corrected normalization coefficient in eqn. 1 and a typo in the definition of wavenumber following eqn. 7. No results were affected by these correction

Counting Abelian Squares for a Problem in Quantum Computing

In a recent work I developed a formula for efficiently calculating the number of abelian squares of length $t+t$ over an alphabet of size $d$, where $d$ may be very large. Here I show how the expressiveness of a certain class of parameterized quantum circuits can be reduced to the problem of counting abelian squares over a large alphabet, and use the recently developed formula to efficiently calculate this quantity

Bright source of spectrally uncorrelated polarization-entangled photons with nearly single-mode emission

We present results of a bright polarization-entangled photon source operating at 1552 nm via type-II collinear degenerate spontaneous parametric down-conversion in a periodically poled potassium titanyl phosphate crystal. We report a conservative inferred pair generation rate of 123,000 pairs/s/mW into collection modes. Minimization of spectral and spatial entanglement was achieved by group velocity matching the pump, signal and idler modes and through properly focusing the pump beam. By utilizing a pair of calcite beam displacers, we are able to overlap photons from adjacent down-conversion processes to obtain polarization-entanglement visibility of 94.7 +/- 1.1% with accidentals subtracted.Comment: 4 pages, 7 color figures. Revised manuscript includes the following changes: corrected pair generation rate from 44,000/s/mW pump to 123,000/s/mW pump; replaced Fig. 1b to enhance clarity; minor alterations to the title, abstract and introduction; grammatical correction

Variational quantum regression algorithm with encoded data structure

Variational quantum algorithms (VQAs) prevail to solve practical problems such as combinatorial optimization, quantum chemistry simulation, quantum machine learning, and quantum error correction on noisy quantum computers. For variational quantum machine learning, a variational algorithm with model interpretability built into the algorithm is yet to be exploited. In this paper, we construct a quantum regression algorithm and identify the direct relation of variational parameters to learned regression coefficients, while employing a circuit that directly encodes the data in quantum amplitudes reflecting the structure of the classical data table. The algorithm is particularly suitable for well-connected qubits. With compressed encoding and digital-analog gate operation, the run time complexity is logarithmically more advantageous than that for digital 2-local gate native hardware with the number of data entries encoded, a decent improvement in noisy intermediate-scale quantum computers and a minor improvement for large-scale quantum computing Our suggested method of compressed binary encoding offers a remarkable reduction in the number of physical qubits needed when compared to the traditional one-hot-encoding technique with the same input data. The algorithm inherently performs linear regression but can also be used easily for nonlinear regression by building nonlinear features into the training data. In terms of measured cost function which distinguishes a good model from a poor one for model training, it will be effective only when the number of features is much less than the number of records for the encoded data structure to be observable. To echo this finding and mitigate hardware noise in practice, the ensemble model training from the quantum regression model learning with important feature selection from regularization is incorporated and illustrated numerically